Direct and inverse scattering problems for two-velocity dynamical systems with time dependent potential

The paper presents an approach to the scattering problem on the half-line for a class of dynamical systems involving two types of waves that propagate at different velocities and interact within a non-stationary medium. The scattering operator on the half-line is defined, and its Volterra property is established. A procedure is then proposed for solving the inverse scattering problem, namely, recovering the time-dependent potential from the scattering operator. This work is inspired by M. I. Belishev et al. (1997), who addressed the reconstruction of a spatially varying potential of the dynamical system coupling two one-dimensional wave equations from scattering data.